Method of tuning a musical tone generator bar



J. T. KUNZ 3,01 METHOD OF TUNING A MUSICAL TONE. GENERATOR BAR Dec. 19, 1961 4 Sheets-Sheet 1 Original Filed Aug. 19, 1955 J INVfiElTiER 7%.,(M 7L. PM

TT Rl lEYs Dec. 19, 1961 J. T. KUNZ 3,013,461

METHOD OF TUNING A MUSICAL TONE GENERATOR BAR Original Filed Aug. 19, 1955 4 Sheets-Sheet 2 CARJLLON BELL.

TONE NAME 55C. OCTAVE FIFTH MAJOR- 'n-mzp Fuzs'r OCTAVE FIFTH MINORTHHZD STRIKE TONE HUM TONE.

UNNOTCHED ROD PARTIA L FREQUENCY N 0 DA L F U HQIJ'I'ER'QE -F .224- .22 4- 2 PARTIAL 2.77% 132 .500 .152 B PARTIAL 5.44 .094- 55s .sss .094 4 'PART1AL 9.0-{ .075 .277 .500 .277 .073 5* PARTIAL lB-H-H .060 .227 .4 9 .4 9.2'I.7.0so GTH'PARTIAL l8 I7-F .O5l J97. 5%..500546192951 0.00 EOFLWHERE azum-lousmp as SATISFIED 00 .500 4 INVENTOR ATTORNEY Dec. 19, 1961 J. T. KUNZ 3,013,461

METHOD OF TUNING A MUSICAL TONE GENERATOR BAR Original Filed Aug. 19, 1955 50 IPARTIAL 4 Sheets-Sheet 3 I U 2 "2 L s .4 L- INVENTOR ATTORNEYS 3,013,461 METHOD OF TUNING A MUSICAL TONE GENERATOR BAR Original Filed Aug. 19, 1955 J. T. KUNZ Dec. 19, 1961 4 Sheets-Sheet 4 5 PARTIAL.

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110;; P I/Q ATTORNEYS 2* 3f 3 o 3 in own 30 23 m5 9.3 m 03 m2 3 mu 3 who 30 m8 Q GROOVE POSITION United States Patent 3,013,461 .METHGD 0F TUNENG A MUSICAL TONE GENERATOR BAR Jacob T. Kunz, Collegeville, Pa., assignor to Schulmerich Electronics, Incorporated, Sellersville, Pa., 21 corporation of Pennsylvania Original application Aug. 19, 1955, Ser. No. 529,548, now Patent No. 2,898,795, dated Aug. 11, 1959. Divided and this application Oct. 10, 1958, Ser. No. 766,465 2 Claims. (Cl. 84-402) This invention relates to electric or electronic musical instruments and their tone generators, and particularly to one for producing cup-shaped or campaniform bell tones.

Various types of tone generators have been used in music instruments, such as bars or rods and other types of vibrating elements for the purpose of generating vibrations. lvlechanical-electrical pick-ups or transducers for translating the vibrations have been employed, the electrical vibrations produced being amplified, modified as needed, and reproduced by a loudspeaker so as to obtain the desired bell note or tones. A campaniform or traditional bell has certain tonal patterns requiring specific vibrations or partials to be present in predetermined relationships in order to obtain a correct and desirable bell tone. It has been difficult in many prior bell tone generators and instruments to produce the required partials in their correct relationship. The partials also must i have the correct strength and duration relationship during the vibration in order to produce a pure bell tone in the loudspeaker. Another problem is to obtain the minor third required in a bell carillon and the hum, strike and first octave in octave relationship.

One of the objects of the invention is to provide an improved tone generator arrangement having partials thereof in octave or desired relationship.

Another object of the invention is to provide a method of tuning a rod to bring various partials thereof into desired relationship.

A further object of the invention is to provide a tone generator means having the desired partials in a single rod.

The term characteristic tone" or note are used in this specification to mean the sound sensation identifying the pitch of the characteristic tone involved to the listener. The term partia will be used herein to mean one particular vibration in the tone generator, whether or not the lowest vibration therein, and whether or not it is in harmonic relation with other partials in the tone generator. Fundamental will be used herein to mean the lowest vibration or partial actually present in the vibrator or tone generator whether or not it is employed. In an instrument of the type concerned herein, when a vibrator is struck and set into vibration in a particular pattern, a person listening to the note produced as a result thereof, will select the characteristic tone identifying the pitch.

In the case of a campaniform or cup-shaped bell, the desired tones include a hum tone, the strike tone or characteristic tone which identifies the pitch of the bell to the listener, the first octave above the strike tone and the fifth tone above the first octave. The minor third above the strike tone also must be present, such being a required characteristic of a true bell note. In the Flemish type bell, the hum tone should be an octave below the strike tone. Thus, the hum tone, strike tone and the first octave tone are in octave relationship. Such a bell also includes the minor third and a fifth above, the first octave. The normal rod does not provide these tones in their correct relationship. It has been found in the analysis of cast bells that the fifth above the strike tone and major third above the first octave contribute but little or nothing to overall tone color of a carillon bell.

In one form of the invention, a free-free rectangular rod or bar is used as the tone generator, the rod being set into vibration by a striker and vibrations picked-up by a mechanical-electrical transducer, amplified, and reproduced by a loud speaker. It was found after extensive work, that by forming grooves across the wide face of the bar at a specific distance from each end of the bar, that octave relationship would be obtained between the hum partial, strike partial and the partial an octave above the strike. The location of said grooves was found to be critical in that they should be between 0.195 and 0.205 times the length of the rod from each of its ends, the distance preferably being 0.2 times the length. The aforementioned location of the groove is particularly applicable to a bar of uniform cross section along the length, but if a bar of non-uniform cross section is used, the grooving location will change as a function of the configuration of the masses in the non-uniform bar. The hum, strike and octave partials then can be obtained from the plane of the face of the bar carrying the grooving. It was further ascertained that the minor third partial above the strike and fifth above the octave or third partial could be obtained if the rod in addition to said grooving was dimensioned to have a width to thickness ratio of 2:1, the grooving being across the wide face. The rod then could be struck on a corner or in a direction angularly disposed relative to the planes of its wide and narrow faces so as to set the rod into vibration in both its wide and narrow directions. The minor third and its octave vibration is obtained from the plane of the narrow face of the bar.

When the rod is arranged so that the vibrations from both the wide and narrow faces are utilized, the pickup up can be placed at an appropriate place adjacent a corner of the rod.

This application is a division of Serial No. 529,548, filed August 19, 1955, now Patent No. 2,898,795, issued August 11, 1959.

These and other objects, features and advantages of the invention will become apparent from the following description and the accompanying drawings which are merely exemplary.

In the drawings:

FIG. 1 is a side view of one of the vibrators or tone generators of the invention.

FIG. 2 is an enlarged section taken along the line 2-2 of FIG. 1, a striker being included.

FIG. 3 is a perspective schematic View of one manner in which the invention can be carried out, the striker being omitted.

FIG. 4 is a representation of the desired tones in a bell.

FIG. 5 is a table showing relation of partials in an unnotched bar.

FIG. 6 is a graph showing the relation of the groove location to a function obtained by use of the curves of FIGS. 7, 8 and 9, the latter curves having as their base, a determination of the effect of changing groove location.

FIG. 10 is a graph showing note or frequency relation to change of groove position for three partials of a notched rod.

The invention may be used with various type musical instruments but will be described specifically conjunction with a bell tone generator for a traditional carillon wherein the hum and strike tone are in octave relationship. As can be seen in FIG. 4, the tones or group of partials for a bell having the pitch C include the hum, strike and first octave partials all in octave relationship and a minor third partial above the strike and a fifth above the first octave. In an untuned bar, the nodal points are indicated in FIG. 5, these not being in the proper relation to each other to produce the desired tones.

A musical instrument embodying the invention may include one or more notes selectively strikable by actu- GD ation of keys from a keyboard. Where one vibrator is employed for each note it may take the form illustrated in FIGS. 1, 2 and 3 wherein rectangular bar Zil may have a Wide face or width W which is twice the width, within narrow limits (5%), of the thickness or narrow face N of the bar. Vibration in the W direction means in the plane of the wide face and in the N direction, in the plane of the narrow face. The required octave relationship between hum, strike and octave above strike partials occurs only when the grooves are cut as described herein with the center or" each groove substantially at a distance 0.2L from each end of the rod.

As mentioned above, a bell tone also must have a minor third above the strike and a fifth above the first octave. it was found that these partials or vibrations could he obtained from the same red by using those from the narrow face when the W and N dimensions of the rod have the correct dimensional relation to each other.

Grooves 21, 2.1 are cut or formed in rod at a location described in detail hereafter. The rod may be supported, for example, by stretched threads or strands 22, said support strands being fastened to frame 23 in any suitable manner. In the illustrated form wherein vibrations from both the W and N faces are to be used, the striker 2d is arranged so that plunger (HG. 2) will strike a corner of the rod 29 or will strike the rod in an angular direction relative to the planes of faces W and N. If the partials from the W face only are to be used, the striker can be arranged to strike the rod in a direction perpendicui r face W. If there are a plurality of rods as in a carillon, each striker can be selectively actuated from a keyboard 27.

A mechanical-electri al pick-up of any suitable type can be located adjacent a corner of the rod so as to pick-up vibrations. The pick-up is illustrated as of the magnetic type but may be a capacitive arrangement. The pick-up is connected through an amplifier 29 to a loud speaker means 30 in the usual manner, the amplifier and speaker being chosen to attenuate partials as needed.

As a result of the discovery, studies were made and it can be theorized that each point on a rod vibrates with simple harmonic motion or y amplitude cos 21ft Where f=frequency and t=time. Substituting, we obtain 21r y=A sin eos 21ft where l=length.

These relations are quite complex for a bar such as a free-free rod and can be expressed by the equation:

y=X(x) cos 21rit wherein Y is the amplitude function, x the coordinate along the rod, and f the frequency.

The set of functions resulting therefrom defining the shape of a vibrating free-free rod is called the set of normal functions for the rod. In ascertaining frequency the potential and kinetic energy relationships can be considered as the rod vibrates. Inertia enters into the problem as well as the modulus of elasticity of the rod material. In a cycle of vibration of a rod, the total energy is at one time all kinetic and at another time all potential. If the shapes of the characteristic functions are known, frequencies can be determined.

If the grooves are made close to the ends of a freefree rod where the displacement is relatively large and curvature small, the tendency would be to increase frequency. If the notches are located where the curvature is large but displacement small, then frequency will decrease. The displacements and curvatures of the bar are different for each of the first three partials.

The expressions for frequency contained in the quantity i p for each of the first three partials for a notched rod can be written:

wherein the moment of inertia relations for a rectangular rod have been substituted in (l), (2) and (3) and 1 a 2 -2 1 m2 and for X21 n for In order to have an octave relation;

P2= P1; 3 2 2- 01 so dividing and solving the following may be written:

l!7(53 2 (a 'fliz ll-l .1Q[(2 '1 )@z fi il The subscripts indicate the partials involved; is the inertia factor, 5 is a second derivative function, 5 is a function, and g is a function of the notched dimension and inertia concerned.

The curves of FIGS. 7, 8 and 9 were determined from r the above formula utilizing the shape of the curves experimentally determined, such as illustrated in FIG. 10. PEG. 10 shows the effect of changing the groove locations relative to the ends of the rod. it is to be noted that for the grooves used in FlG. 10, the first three partials are in octave relationship when the grooves are at a position 0.2L, the distances X and Y being substantially equal. The curves were obtained by plotting results obtained from a stroboscope. A plurality of identical rods were selected. The cross sectional area of each rod was changed at locations from each end thereof by grooving. The location of the grooving was at a dimension equidistant from the ends of each bar, the dimension being different for each of the bars. Each of the bars was struck and the vibrations thereof electrically picked up and amplified. The stroboscope was used to determine the pitch of at least three of the partials existent in each bar, and these partials were graphically represented or plotted, as in FIG. 10, in the Y direction in relation to the grooving or cross sectional alteration dimension in the X direction. The partial relationship or intervals between the partials can be selected from the curves by measuring or otherwise and the groove location read from the curve required to produce the desired partial relationship.

Equation 7 cannot be solved numerically but can be determined graphically as is plotted in PEG. 6, the crossing of the 0 axis being the value of x where satisfied.

in FIG. 6 several curves are plotted for slightly varying groove characteristics in rods found to be satisfactory and it can be seen that octave relationship is obtained when the grooves are located from the end of the bar in the range of 0.195 and 0.205 of the length thereof. The notch factors used were chosen to represent various web thickness, these representing relative variations in bar thickness (N) to the thickness of the 'bar at the notch (a, FIG. 2).

The rods involved were made of steel inasmuch as a magnetic pick-up or transducer was employed but other materials can be used in accordance with the pick-up arrangement.

It is to be understood that the invention can be used in conjunctionwith picking up vibrations from only the wide face as well as the combination of vibrations. Also, it should be obvious that variations may be made in details of construction and procedure without departing from the spirit of the invention except as defined in the appended claims.

I claim:

1. The method of tuning an electric music instrument tone generator bar so that the bar will have a desired partial relationship between the frequencies of vibrations therein when the bar is set into vibration, comprising the steps of selecting a group of identical bars, altering the cross-sectional area of each of said identical bars at two points at a dimension equidistant from the ends of each bar, said dimension being different for each bar of said group of bars, mounting each one of said bars of said group separately and in free-free relation, striking each of said bars separately to produce mechanical vibrations therein, electrically picking up and amplifying a plurality of partials from a bar that has been struck, measuring the frequencies of more than one of the amplified partials present in a bar when struck, graphically representing the relation of said measured amplified partials in each bar of said group to the dimension from the ends of the bar of the altered cross-sectional area, then determining from said graphical representation, the dimension of the altered cross-sectional area from each end of the first mentioned bar to provide the desired interval between partials, and

altering in accordance with said graphical representation, the cross section of the first mentioned bar, at two points equidistant from the ends of said bar at the dimension, as determined, to provide the desired relationship of partials in said bar.

2. The method of tuning a bar to desired partial relationship for use in an electric musical instrument, comprising the steps of selecting a plurality of identical bars, altering the cross-sectional area of each of said identical bars at two points at a dimension equidistant from the ends of each bar, said dimension being diiferent for each of said plurality of bars, mounting each one of said plurality of bars separately and in free-free relation, striking each of said bars separately, electrically picking up and amplifying a plurality of partials from each of said plurality of bars, measuring a plurality of the amplified partials present in the vibration of each bar, graphically representing the relation of the dimension from the ends of each bar of the altered cross-sectional area in the X direction to the plurality of the partials in the Y direction produced by each bar when struck, selecting the distances in accordance with said graph between partials which will give the desired relation between partials, matching said distances on said graph in a Y direction to locate the dimension from the ends of said bar where the crosssectional area is to be altered to provide the selected relationship, and then altering the cross section of the first mentioned bar at two points equidistant from the ends of said bar to provide the desired partial relationship in the bar being tuned.

References Cited in the file of this patent UNITED STATES PATENTS 2,273,333 Schluter Feb. 17, 1942 2,352,438 Hruby June 27, 1944 2,606,474 Kunz Aug. 12, 1952 2,655,069 Marshall Oct. 13, 1953 2,727,423 Meeker et al Dec. 20, 1955 UNITED STATES PATENT OFFICE Certificate of Correction Patent No. 3,013,461 December 19, 1961 i Jacob T. Krmz It is hereby certified that error appears in the above numbered patent requiring correction and that the said Letters Patent should read as corrected below.

Column 1, line 66, strike out the comma; column 2, line 33, for pickup read pick-up; line 34, strike out up; column 4, lines 4, 7 and 10, the three formulae should have denominators under 8AX to read, respectively:

f l l fgl z fgl z column 4, lines 31 to 33 should appear as shown below instead of as in the patent:

11 i 2 Z? 5 for X 1 and 5 for X 1 Signed and sealed this 24th day of December 1963.

[SEAL] Attest:

ERNEST W. SlVIDER, EDWIN L. REYNOLDS, Attestz'ng Oyficer. Acting Commissioner of Patents.

UNITED STATES PATENT OFFICE Certificate of Correction Patent No. 3,013,461 December 19, 1961 I i Jacob T. Kunz It is hereby centified that error appears in the above numbered patent requiring correction and that the said Letters Patent should read as corrected below.

Column 1, line 66, strike out the comma; column 2, line 33, for pickup read pick-up-; line 34, strike out up; column 4, lines 4, 7 and 10, the three formulae should have denominators under 8AX to read, respectively:

fu z

YZZZZ column 4, lines 31 to 33 should appear as shown below instead of as in the patent:

5 for X 1 6x2 and 5 for X 1 Signed and sealed this 24th day of December 1963.

[SEAL] Attest:

ERNEST W. STVIDER, EDWIN L. REYNOLDS, Attesting Ofiicer. Acting Commissioner of Patents. 

